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Abstract Dynamic chaos is a very interesting non-linear effect, which has been intensively studied since Lorenz found the first canonical chaotic attractor in 1963. The effect is very common, it has been detected in a large number of dynamic systems of various physical natures, so it always says ”Most” physical systems are chaotic. In practice, chaos may be desirable or undesirable depending on the applications. In combustion application, chaos is desirable because it enhances mixing of air and fuel and hence leads to better performance. More over it has been utilized in many other practical applications such as increasing the power of lasers, synchronizing the output of electronic circuits, increasing the heat exchange, improving the performance of mobile robot and encode electronic messages for secure communications On the other hand, in aerodynamic and hydrodynamic applications, chaos (turbulence) is undesirable because it dramatically increases the drag of vehicles and results in increased operational cost. In mechanical and structural systems chaos may lead to irregular operation and fatigue failure. More over chaos can restrict the operating range of many mechanical and electronic devices. A chaotic system is a highly complex dynamic nonlinear system that possesses some special features like excessive sensitivity to initial conditions, transitivity and it possesses a dense set of bounded but typically unstable periodic orbits (UPO), which a non-chaotic nonlinear system generally does not have. As a result of its dependence on initial conditions, one can conclude that chaos control is not possible. Thus, to take advantage of chaos, controlling a chaotic orbit to reach a particular UPO is beneficial some engineering applications. This motivates the current research in controlling UPO of chaotic systemsChaos control, in a broader sense, can be divided into two categories: • Suppress the chaotic dynamical behavior where chaotic behavior is irregular, complex and generally undesirable. • Generate or enhance chaos in nonlinear systems to be used in the above mentioned applications such as secure communications. The main objective of this thesis is to design a controller that is able to mitigating or eliminating the chaos behavior of nonlinear systems that experiencing such phenomenon. Three approaches are proposed for chaos control. The first is ”Controlling chaotic systems via time-delayed control”. Based on Lyapunov stabilization theory a proportional plus integral timedelayed controller is proposed to stabilize UPOs embedded in chaotic attractors.The second is ”Adaptive sliding mode control for a class of chaotic systems”. An Adaptive Sliding Mode Controller (ASMC) is presented based on Lyapunov stability theory. The robustness of the proposed scheme is proved, even in the presence of parametric uncertainties. The third is ”An adaptive feedback control for a class of chaotic systems”. A new scheme of adaptive control based on predetermined control signal to stabilize UPOs embedded in chaotic attractors is proposed. The predetermined control signal is constructed based on time-delayed. The adaptation law is derived based on Lyapunov stabilization theory. This thesis is constructed of seven chapters, the first chapter describes the meaning of chaos, the difference between chaos and randomness, the properties of chaotic systems and finally answers the question that say, why chaos control? The answer is provided with real applications of chaos control, which include chaotic mobile robot, chaotic mixing, secure communication, and other applications. Three conventional control techniques for chaos control including dislocation, enhancing and speed feedback is discussed in chapter two. Adaptive time delay control for chaotic systems is discussed in chapter three. At first, advantages and disadvantages of time delay feedback control isdiscussed then varies control techniques based on time delayed for chaos is discussed such as ”Adaptive Iterative Learning strategy”, ”repetitive Learning strategy”, ”successive dislocation feedback strategy and then Proportional plus integral strategy”. Integrity control of chaotic systems in the case of sensors failure only is discussed in chapter four. This controller is considered as a type of fault tolerant control of chaos. Sliding mode control (SMC) and adaptive sliding mode control (ASMC) are discussed in chapter five. At first, the main concepts of SMC is given then varies control techniques are given for chaos control based on SMC and ASMC such as, ”proportional plus integral sliding surface”, ”adaptive sliding mode control”, ”global adaptive sliding mode control”, ”adaptive proportional-integral switching surface” and then ”sliding surface based on delayed feedback”. Two methods of chaos control is discussed in chapter six, the first is dealing only with the linearized chaotic systems that satisfy certain form but the second dealing with a form that satisfied by almost chaotic systems. In the two methods, a predetermined control signal is considered, and then the feedback control gains are obtained. Some conclusions are given in chapter seven, followed by future works then all published, accepted and submitted papers related to chaos control and synchronization are listed in the last.. |